Multi-view dimensionality reduction learning with hierarchical sparse feature selection

Multi-view data can depict samples from various views and learners can benefit from such complementary information, so it has attracted extensive studies in recent years. However, it always locates in high-dimensional space and brings noisy or redundant views and features into the learning process, which can decrease the performance of the learner. To address the above issue, we propose a novel unsupervised Multi-view Dimensionality Reduction learning framework with Hierarchical Sparse Feature Selection (MvDRHSFS) to learn a low-dimensional subspace by jointly selecting the most informative views and features hierarchically. More specifically, we penalize the projection matrix with Frobenius norm (F-norm) and l(2,1)-norm to select the most informative views and features hierarchically. Under the penalty of the two regularization terms, some projection-based Sigle-view Dimensionality Reduction (SvDR) methods can learn a more meaningful low-dimensional subspace of multi-view data. In practical implementation, we use the regression type of PCA and relax the orthogonal constraint of the projection matrix to learn the low-dimensional subspace in a more flexible way. To find the optimal solution of the proposed learning framework, we derive an effective way to optimize the given formulation and give the theoretical analysis about the convergence for the optimization algorithm. Extensive experiment results on several real-world datasets demonstrate the feasibility and superiority of our proposed learning framework.